
where \((\mathbf {x},\mathbf {y})\)  denotes the scalar product of two vectors \(\mathbf {x},\mathbf {y}\in \mathbb {R}^n\) , and \(S^{n-1}\)  is the unit sphere in \(\mathbb {R}^n\) .
The measure \(\Gamma \)  is called the spectral measure of \(\mathbf {X}\) . It is unique, finite and symmetric for \(0<\alpha <2\)  [1]}.
A random variable \(X\in L^0_c(\Omega )\)  has complex symmetric \(\alpha \) -stable distribution if its real and imaginary parts form a \(S\alpha S\)  random vector, i.e. if the vector \((Re(X),Im(X))\)  is jointly \(S\alpha S\) .
